Using wavelet transforms for multiresolution materials modeling

Computers and Chemical Engineering

Volumn 29, Issue 4, 2005, Pages 689-700

  Ismail, Ahmed E ^a   Rutledge, Gregory C ^a   Stephanopoulos, George ^a  

^a Massachusetts Institute of Technology   (United States)

Author keywords

Ising model; Lattice gas; Molecular simulation; Self avoiding walks; Wavelets

Indexed keywords

COMPUTER SIMULATION; MATERIALS HANDLING; MATHEMATICAL MODELS; MONTE CARLO METHODS; POLYMERS;

ATOMISTIC SIMULATIONS; ISING LATTICES; SAMPLING MECHANISMS;

WAVELET TRANSFORMS;

POLYMER;

MODELING;

ACCURACY; MATHEMATICAL MODEL; MONTE CARLO METHOD; PHYSICAL CHEMISTRY; QUALITATIVE ANALYSIS; QUANTITATIVE ANALYSIS; REVIEW; SAMPLING; SIMULATION;

EID: 15944368273     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compchemeng.2004.09.015     Document Type: Article

References (42)

1. Best, C. (1999). Wavelet-induced renormalization group for the landau-ginzburg model. http://xxx.lanl.gov/abs/hep-lat/9909151.
2. Best, C., Schäfer, A. (1994). Variational description of statistical field theories using Daubechies' wavelets. http://xxx.lanl.gov/abs/hep-lat/ 9402012.
3. C. Best, A. Schäfer, and W. Greiner Wavelets as a variational basis of the XY model Nuclear Physics B: Proceedings Supplements 34 1994 780 782
4. I. Carmesin, and K. Kremer The bond fluctuation method: A new effective algorithm for the dynamics of polymers in all spatial dimensions Macromolecules 21 1988 2819 2823
5. Chou, K. C. -K. (1991). A stochastic modeling approach to multiscale signal processing. Ph.D. thesis. Massachusetts Institute of Technology.
6. T.H. Cormen, C.E. Leiserson, and R.L. Rivest Introduction to algorithms 1990 McGraw Hill-MIT Press Cambridge, MA
7. S. Curtarolo, and G. Ceder Dynamics of an inhomogenously coarse grained multiscale system Physical Review Letters 88 2002 255504
8. Daubechies, I. (1992). Ten lectures on wavelets. In Proceedings of the CBMS-NSF Regional Conference Series in Applied Mathematics (Vol. 61). SIAM, Philadelphia.
9. J. Dautenhahn, and C.K. Hall Monte Carlo simulation of off-lattice polymer chains: Effective pair potentials in dilute solution Macromolecules 27 1994 5399 5412
10. P. Español Hydrodynamics from dissipative particle dynamics Physical Review E 52 1995 1734 1742
11. D. Frenkel, and B. Smit Understanding molecular simulation: From algorithms to applications 1996 Academic Press San Diego
12. D. Gines, G. Beylkin, and J. Dunn LU factorization of non-standard forms and direct multiresolution solvers Applied and Computational Harmonic Analysis 5 1998 156 201
13. N. Goldenfeld Lectures on phase transitions and the renormalization group 1992 Addison-Wesley Reading, MA
14. J. Goodman, and A.D. Sokal Multigrid Monte Carlo method for lattice field theories Nuclear Physical B: Proceeding Supplements 56 1986 1015 1018
15. J. Goodman, and A.D. Sokal Multigrid Monte Carlo method. Conceptual foundations Physical Review D 40 1989 2035 2071
16. A. Haar Zur Theorie der orthogonalen Funktionen-Systeme Mathematische Annalen 69 1910 331 371
17. B.D. Hughes Random walks and random environments 1995 Oxford-Clarendon Press New York
18. Irving, W. W. (1995). Multiscale stochastic realization and model identification with applications to large-scale estimation problems. Ph.D. thesis. Massachusetts Institute of Technology.
19. A.E. Ismail, G.C. Rutledge, and G. Stephanopoulos Multiresolution analysis in statistical mechanics. I. Using wavelets to calculate thermodynamic properties Journal of Chemical Physics 118 2003 4414
20. A.E. Ismail, G. Stephanopoulos, and G.C. Rutledge Multiresolution analysis in statistical mechanics. II. The wavelet transform as a basis for Monte Carlo simulations on lattices Journal of Chemical Physics 118 2003 4424 4431
21. L.P. Kadanoff Statistical physics: Statics, dynamics, and renormalization 2000 World Scientific Singapore
22. M.A. Katsoulakis, A.J. Majda, and D.G. Vlachos Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems Journal of Computational Physics 186 2003 250 278
23. M.A. Katsoulakis, and D.G. Vlachos Coarse-grained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles Journal of Chemical Physics 119 2003 9412 9427
24. T. Kennedy A faster implementation of the pivot algorithm for self-avoiding walks Journal of Statistical Physics 106 2002 407 429
25. M. Lal ''Monte Carlo'' computer simulation of chain molecules. I Molecular Physics 17 1969 57 64
26. D.A. Lavis, and G.M. Bell Statistical mechanics of lattice systems 1: Closed-form and exact solutions 1999 Springer Berlin
27. A.A. Louis, P.G. Bolhuis, J.-P. Hansen, and E.J. Meijer Can polymer coils be modeled as ''soft colloids''? Physics Review Letters 85 2000 2522 2525
28. M.R. Luettgen, W.C. Karl, A.S. Willsky, and R.R. Tenney Multiscale representations of Markov random fields IEEE Transactions on Signaling Process 41 1993 3377 3396
29. S.-K. Ma Modern theory of critical phenomena 1976 Benjamin/Cummings Reading, MA
30. S.-K. Ma Renormalization group by Monte Carlo methods Physics Review Letters 37 1976 461 464
31. N. Madras, and A.D. Sokal The pivot algorithm - a highly efficient Monte-Carlo method for the self-avoiding walk Journal of Statistical Physics 50 1988 109 186
32. A.A. Migdal Recursion equations in gauge field theories Soviet Physics JETP 42 1976 413 418
33. L. Onsager Crystal statistics 1: A two-dimensional model with an order-disorder transition Physical Review 65 1944 117 149
34. R.K. Pathria Statistical mechanics 1996 Butterworth-Heinemann Woburn, MA
35. G.S. Pawley, R.H. Swendsen, D.J. Wallace, and K.G. Wilson Monte Carlo renormalization-group calculations of Physical Review B 29 1984 4030
36. A.G. Schlijper, P.J. Hoogerbrugge, and C.W. Manke Computer simulation of dilute polymer solutions with the dissipative particle dynamics method Journal of Rheology 39 1995 567 579
37. G. Strang, and T. Nguyen Wavelets and filter banks 1996 Wellesley-Cambridge Cambridge, MA
38. W. Sweldens The lifting scheme: A new philosophy in biorthogonal wavelet constructions A.F. Laine M. Unser Wavelet applications in signal and image processing III. Proceedings SPIE 2569 1995 68
39. W. Sweldens The lifting scheme: A construction of second generation wavelets SIAM Journal on Mathematical Analysis 29 1997 511
40. R.H. Swendsen Monte Carlo renormalization group Physics Review Letters 42 1979 859 861
41. K.G. Wilson Renormalization group and critical phenomena. I. Renormalization group and the Kadanoff scaling picture Physical Review B 4 1971 3174 3183
42. K.G. Wilson Renormalization group and critical phenomena. II. Phase-space cell analysis of critical behavior Physical Review B 4 1971 3184 3205